Birds, bugs and rodents serve the purpose of easing new players into the game. It's the sort of creatures you'd find in your back yard. Small animals, which don't really stand out, and are easily captured/domesticated. Only later do you get to see the exotic creatures the world of Pokémon has to offer, and "unlock" the more exciting and powerful monsters. The first Pokémon you find are the baby steps of your journey, barely walking into the woods outside your town, where the most mundane creatures live.
The bugs serve the double purpose of showcasing evolution very early on and in an intuitive way. Larvae - pupae - fully evolved whatever. They evolve quickly, and become noticeably stronger once they reach their final form. They show that this is how most Pokémon grow. If memory serves me correctly, all the Pokémon found in the first few routes of every game will evolve at least once.
With a few exceptions, the early game Pokémon are nearly always very "basic" types with simple type chart interactions. The usual FGW triangle, Normal types which hit and take hits for normal damage (for now), Bugs which are burned by fire and eat plants, Flying creatures that eat bugs and plants. Only later will you see the more complex and less intuitive interactions between types such as Psychic, Ice, Dragon, Rock and Ghost.
With all that being said, the designers are kind of limited on options when designing early-game Pokémon. They have to be "back yard" creatures, they have to evolve somewhat early, they have to have "simple" types with intuitive type chart interactions, and they can't be so strong that they outpower the Pokémon you meet later - after all, the designers want you to try out a variety of Pokémon, incentivizing you to swap out your first few captures when their power level starts to wane mid-game. Also, they have to make new Pokémon for every generation, since you want long-time fans to feel that something new is happening, with new creatures, locations and moves. Reusing older designs won't do, after all the players should feel that the new game they bought does include new content.